"Deflationism and Conservativity"Lavinia Picollo (Munich Center for Mathematical Philosophy)
2017 Salzburg-Irvine-Munich Workshop in Logic and Philosophy of Science: In the Sciences
HIB 55, Department of Philosophy, Enter Conference from the Philosophy Department Entrance
55 Humanities Instructional Building
University of California, Irvine 92697-4555
- Department of Philosophy
- School of Social Sciences
A wide variety of claims is often associated with deflationism about truth, including the idea that truth is metaphysically thin, not a substantial property. This has been interpreted by Shapiro, Ketland, Field, and others as asserting that truth has no explanatory power, which in turn, has been taken to mean that axiomatic truth theories should be conservative over their respective base systems. This is problematic as many intuitively appealing truth theories violate the conservativity requirement. As a consequence, the deflationist position is often deemed untenable. We argue that this line of reasoning is fundamentally misguided, as it draws upon a misconception of deflationism. We first provide a historical account of deflationism, based on which we put forward a rational reconstruction of the actual position. According to this rational reconstruction, the main theme of deflationism is that the truth predicate’s only purpose in natural language is to emulate higher-order quantification within first-order single-sorted languages. We argue that metaphors such as “truth is not a substantial property” are meant to emphasise that truth is a property that is expressed by a mere logical or quasi-logical (depending on how higher-order quantification is to be understood) expressive devise, and nothing more. As a consequence, we should not rush into concluding that truth cannot have any explanatory power, or that axiomatic truth theories must be conservative over their corresponding base systems. We maintain that, according to deflationism, truth should have as much explanatory power as higher-order logics do, and truth theories should be as conservative as higher-order logics are. In the light of the well-known results of non-conservativity of, e.g. second-order arithmetic over its first-order counterpart, we conclude that deflationists are not committed in any way to adopting conservative theories of truth.
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